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Part A: Factor 2x2y2 + 6xy2 + 18x2y2. Show your work.

Part B: Factor x2 + 10x + 25. Show your work.

Part C: Factor x2 − 36. Show your work.

User Zdebra
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1 Answer

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Answer:

A.


2xy^2(10x+3)

B.


(x+5)^2

C.


(x-6)(x+6)

Explanation:

Part A. The expression
2x^2y^2+6xy^2+18x^2y^2 consists of three terms:
2x^2y^2,\ \ 6xy^2,\ \ 18x^2y^2 The first and the last terms are like terms, we can add them:


2x^2y^2+18x^2y^2=20x^2y^2

Now,


20x^2y^2=2xy^2\cdot 10x\\ \\6xy^2=2xy^2\cdot 3

So,


2x^2y^2+6xy^2+18x^2y^2=2xy^2(10x+3)

Part B. The expression
x^2+10x+25 is a square of
x+5, so


x^2+10x+25=(x+5)^2

Part C. Use the difference of squares formula:


x^2-36=x^2-6^2=(x-6)(x+6)

User Jonas Zaugg
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